From dice to modern electronic circuits, there have been many attempts to build better devices to generate random numbers. Randomness is fundamental to security and cryptographic systems and to safeguarding privacy. A key challenge with random-number generators is that it is hard to ensure that their outputs are unpredictable. For a random-number generator based on a physical process, such as a noisy classical system or an elementary quantum measurement, a detailed model that describes the underlying physics is necessary to assert unpredictability. Imperfections in the model compromise the integrity of the device. However, it is possible to exploit the phenomenon of quantum non-locality with a loophole-free Bell test to build a random-number generator that can produce output that is unpredictable to any adversary that is limited only by general physical principles, such as special relativity. With recent technological developments, it is now possible to carry out such a loophole-free Bell test. Here we present certified randomness obtained from a photonic Bell experiment and extract 1,024 random bits that are uniformly distributed to within 10. These random bits could not have been predicted according to any physical theory that prohibits faster-than-light (superluminal) signalling and that allows independent measurement choices. To certify and quantify the randomness, we describe a protocol that is optimized for devices that are characterized by a low per-trial violation of Bell inequalities. Future random-number generators based on loophole-free Bell tests may have a role in increasing the security and trust of our cryptographic systems and infrastructure.

We implement D7 flavor branes in AdS-sliced coordinates on AdS5 × S 5 with the ansatz that the brane fluctuates only in the warped (µ) direction in this slicing, which is particularly appropriate for studying the Janus solution. The natural field theory dual in this slicing is N = 4 super Yang-Mills on two copies of AdS4. Branes extending from µ = ±π/2 can end at different locations, giving rise to quarks with piecewise constant mass on each AdS4 half-space, jumping discontinuously between them. A second class of flavor brane solutions exists in this coordinate system, dubbed "continuous" flavor branes, that extend across the entire range of µ. We propose that the correct dual interpretation of "disconnected" flavor brane in this ansatz is a quark hypermultiplet with constant mass on one of the AdS4 half-spaces with totally reflecting boundary conditions at the boundary of AdS4; whereas the dual interpretation of a continuous flavor brane has totally transparent boundary conditions. Numerical studies indicate that AdS-sliced D7 flavor branes of both classes exhibit spontaneous chiral symmetry breaking, as non-zero vev persists for solutions of the equation of motion down to zero mass. Continuous flavor branes in this ansatz exhibit many other surprising behaviors: their masses seem to be capped at a modest value near m = 0.551 in units of the inverse AdS radius, and there may be a phase transition between continuous branes of different configurations. We also numerically study quark states in Janus. The behavior of mass and vev is similar in Janus, including the existence of chiral symmetry breaking at zero mass, though qualitative features of the phase diagram change (sometimes significantly) as the Janus parameter c0 increases.